hal@rain.org wrote:
>
> Eugene Leitl apparently wrote:
> >
> > http://cvm.msu.edu/~dobrzele/dp/
> >
> > I'm exstatic. They have a mailing list. They have a bibliography.
> >
> > This is how I found this gem here:
> > http://xxx.lanl.gov/html/physics/9810010
> >
> > SPECIAL RELATIVITY DERIVED FROM CELLULAR AUTOMATA THEORY:
> >
> > The origin of the universal speed limit
>
> I am reading this CA paper, and I have a couple of concerns about it.
>
> The main claim of deriving special relativity from CA theory is in
> section 9. They say:
>
> : Special Relativity theory is founded on two basic postulates:
> :
> : (1) The velocity of light in a vacuum is constant and is equal for all
> : observers in inertial frames (inertial frame is one in which Newton?s
> : law of inertia is obeyed).
> :
> : (2) The laws of physics are equally valid in all inertial reference
> : frames.
>
> which is OK. But they claim that there is no explanation of why (1) is
> true in terms of (2). Actually from what I understand (1) follows from
> (2). The Maxwell equations for electromagnetism predict the existence
> of EM waves which travel at a speed determined by various properties
> of the vacuum. If you measure those properties the speed works out to
> c, the speed of light. Hence Maxwell's equations predict that light
> propagates at a speed of c. If you assume (2) then it will propagate
> at c in all inertial frames, hence (1) follows.
>
> Now, here is their explanation for (2) in terms of the universe as a CA:
>
> : The second postulate of special relativity states that the laws of
> : physics are equally valid in all inertial reference frames. Stated
> : in a weaker form, there are no preferred reference frames to judge
> : absolute constant velocity motion (or inertial frames). This latter
> : form is easily explained in CA theory, by remembering that all cells
> : and their corresponding rules in the cellular automata are absolutely
> : identical everywhere. Motion itself is an illusion, and really represents
> : information transfers from cell to cell. To assign meaning to motion
> : in a CA, one must relate information pattern flows from one numeric
> : pattern group with respect to another group (the actual cell locations
> : are inaccessible to experiment). Therefore, motion requires reference
> : frames. Unless you have access to the absolute location of the cells,
> : all motion remains relative in CA theory. In other words, there is no
> : reference frame accessible by experiment that can be considered as the
> : absolute reference frame for constant velocity motion.
>
> This is so vague as to be meaningless. There is no reference to any
> properties of the CA other than that it can let patterns "flow" from
> place to place (somewhat like gliders in Conway's Life). Does it really
> follow from this very general property that the laws of physics would
> be the same in all reference frames? Just because patterns can flow,
> it follows that absolute velocity can't be detected, and that physics
> is the same for all uniform observers? I don't think so.
>
> Light, in their model, is a disturbance propagating at the maximum
> speed of one cell per tick in the CA. And in fact CA workers often
> do refer to one cell per tick as "the speed of light" by analogy to
> relativity theory. In section 9.3 the authors attempt to show that
> all uniformly moving observers will measure the speed of light to be
> the same in all directions. But again I didn't find the argument clear
> or persuasive. For one thing, it would seem that the geometry of the
> CA array should be relevant. In a three dimensional cubic geometry CA
> (which they choose without discussing other polyhedral geometries),
> disturbances can propagate faster in the diagonal direction than along
> the axes. Living in such a CA would seem to give a set of preferred
> directions. They don't seem to discuss this effect. They don't have
> a clear definition of how clocks and rulers would be expected to work,
> making it hard to interpret their explanations of what people would see.
>
> Overall I can't help feeling that they have jumped past the hard parts
> with some handwaving and vague arguments. If the universe is a CA, it
> would seem that there ought to be some constraints on the properties it
> would have. Their arguments would apply to virtually any CA, and that
> can't be right.
>
> Hal
--
"Knowing the path is not the same as walking the path."
-Morpheus _The Matrix_